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Computed tomography (CT) is widely used in scientific imaging systems such as synchrotron and laboratory-based nano-CT, but acquiring full-view sinograms requires high radiation dose and long scan times. Sparse-view CT reduces this burden…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…
Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…
In this paper, we present an analytical model for a diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The time-varying spatial distribution of the information molecules under the…
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…
Cone-beam computed tomography (CBCT) is an imaging modality widely used in head and neck diagnostics due to its accessibility and lower radiation dose. However, its relatively long acquisition times make it susceptible to patient motion,…
Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral operator. As a consequence, it finds applications in the…
Nowadays, denoising diffusion probabilistic models have been adapted for many image segmentation tasks. However, existing end-to-end models have already demonstrated remarkable capabilities. Rather than using denoising diffusion…
Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D…
Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or…
Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate…
Several recent papers have studied lensing of the CMB by large-scale structures, which probes the projected matter distribution from $z=10^3$ to $z\simeq 0$. This interest is motivated in part by upcoming high resolution, high sensitivity…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…